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F(x)sin X CesX ~aX < 0X + sin XX7 0findalltKValues#aat Mkefu) dif ferentiablc at X : 0...

Question

F(x)sin X CesX ~aX < 0X + sin XX7 0findalltKValues#aat Mkefu) dif ferentiablc at X : 0

f(x) sin X CesX ~a X < 0 X + sin X X7 0 find all tK Values #aat Mke fu) dif ferentiablc at X : 0



Answers

Determine $a, b$ and $c$ for which the function $f(x)=\frac{\sin (a+1) x+\sin x}{x}, x<0$ $=c, \quad x=0$ $=\frac{\left(x+b x^{2}\right)^{\frac{1}{2}}-x^{\frac{1}{2}}}{b x^{\frac{2}{2}}}, \quad x>0$

Talk about a problem. See, Is that FX's equal? You're saying spread its was Jesus a Knicks, this one. So order the right is it's dropped, refusing on fire. So when we talk about a new life, somewhere here was over here you have just six. She fired last night. So the party asks Sensible graphics. Izabela zero means the X intercepts. We can see that we have one. Do you treat like three x intercepts? So the values of excess seven by was six. She 9 11 was just Barbie is whether function is positive or just above the X axis. So we have This is one part and this is other park. So we have X is an element of 075 or six. Union 11 viral sits. This is the solution for FX is sexist. That benefits this positive when you don't good rules for Tunisia, which is a fixes negative. So you have This is one kiss and this is that Lucas. So we have excess an element or seven by or six too cheap. You again, you haven't. Violence is so This is the solution for FX

Stoppable problem. 51 fix in this case is since critics or six minus classics graphics order the rate in the first bar, we gotta find the points we had a 60 So this means we have to find X intercepts of clearly one and never to x intercepts or excess by working and three while working the next part, we have to find ah region very effects of spas. It means it is about back sexes. Clearly, in this region, it is about act sexist. We say their exes an element off fireworks too and triple minded were not included by about two entry power. There were used open brackets because at those point that fixes not positive and see like ways artsy affects lessons. You know, we have to find the region very fixes below decks, accents. So we have. This is one region and this isn't the region. So the right X is an element off. We can include zero. Why? Because act zero ethics is integrated. So we have zero comma by work to junior tripper worked again. We can prove to buy because the value of to place minus one. So this is the solution for effects lessons

So the derivative of if with respect to X is equal to the derivative of science X. Which is caused X. Uh Plus the derivative of course X which is negative. Sine X. So now if we're looking for the derivative of if with respect to X equals to zero, we just equate cause X minus cynics Equals to zero. So if we add sign X on both sides. Mhm. This will become course X equals two. Sign X. And if you divide by course take on both sides. This will be one equals 2. 10 eggs. Right now, X will be equal to the inverse of 10 evaluated at one. Uh the inverse of 10 and one. So this will be equals two. Um Pi over four. So we know that 10 is actually positive in the first quadrant and the quadrant. So we already have our reference angle here. So to find the angle um to find the angle on the third quadrant, we are just going to say hi. Plus how about for? And this would be equals 2. 5 high over full. Right so X. Mm. Mhm. So X is he calls to however for Um five pi over four. All right, moving on. So we first need to find the derivative um of F of X with respect to X. So we already know that this is cause X minus sine X. So that means that if we want to find a derivative of um F of X with respect to X greater than zero. We just say because X minus sine X Is greater than zero. We do the same as before. So if we add some excellent both sides we end up with of course X greater than sin X. If we divide by cause X on both sides we end up with one greater than 10 x. So let me rewrite that is 10 X less than one. Now if you take the invest of 10 on both sides this will be X less than The inverse of 10 one. Okay. And we are told that the interval of access between zero and two pi Yeah. Hence the derivative of F of X greater than zero. Um It's true on the interval zero hi with before union Or rather all five pi over four two pi Because earlier we already found um these two routes. Yeah. So again We need to find the derivative of 85 X. Which you already know to be uh Cause X minus sine X. Right? So now the derivative of F of X less than zero will be cause X minus sine X less than zero. And we do what we did last time we had signed on both sides we end up with um Sign X. I will end up with cause X less than sign X divide by cause X on both sides. Okay. And we end up at one. Less than 10 x. So this is 10 x greater than one. Now. We make extra subject of formula by applying the interest of 10 on both sides. So we'll have X Greater than the increase of 10 one. Okay. So we know that X has a restriction between zero and two pipe. And we know that this inequality is true um When X is between um biographer, because we already found the roots In between five pi over four. So the derivative of F X less than zero? Yeah. Um It's true. An interval hi over four. Mhm five Pi over four. Okay.

Stoppable problem. 26. So the wishing given us her fixed busy do se Knicks This one. Okay, so a zoo should go find chicken dishes. Let's talk about the party rtc's that you go to find the parts that fixes you. So what are the right? We see the cough, actually. Craft of the secretions or Mexico zero Miss Tax intercepts Their points One is this and oneness, this has a investment. So these other points where affects is equal proceeded. So the ridiculous morning while use off x 75 or six and 11.6 these other points made fixes you? Barbie asked the board graphics is positive. So anything which is above XX is so we have from 07 Fire was six s positive on 11 hours. Six skill who? Pipe up. I will be somewhere here. So 11 by was six to Dubai is also so we did that X is in a limit zero through seven. Fire was since union 11 by six to buy. And next one lost partners we have aboard Benefits is negative so far where her office below the x axis. Clearly it is between these two points. So we write that excess an element of 75 or six. Do we live in violence? Is this is


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